Question

Assume that a simple random sample has been selected and test the given claim. Identify the null and alternative? hypotheses, test? statistic, P-value, and state the final conclusion that addresses the original claim. Listed below are brain volumes in cm cubed cm3 of unrelated subjects used in a study. Use a 0.01 0.01 significance level to test the claim that the population of brain volumes has a mean equal to 1100.9 1100.9 cm cubed cm3. list of brain volumes in cm3 963,1028,1271,1080,1069,1173,1066,1347,1099,1205 identify test statistic t= round 3 decimal places

Answer 1

here we want to find t test statistic for testing population mean of one variable.

Here we want to test the claim that the population of brain volumes has a mean equal to 1100.9 cm cubed cm3

From the claim the null hypothesis

and the alternative hypothesis   

Let's use minitab:

Step 1) First enter the given datase in minitab columns

Step 2) The command is Stat>>>Basic Statistics >>1 sample t...

Select Sample in columns:

then click on Perform hypothesis test enter hypothesis mean (1100.9)

Look the following image:

then click on Option select level of confidence = (1 - alpha)*100 = (1 - 0.01)*100 = 99.0

Alternative " not equal to"

then click on Ok

We get the following output

From the above output

t test statistic value = 0.79

p- value = 0.452

Decision rule: 1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.452 > 0.01 so we used 2nd rule.

That is we fail to reject null hypothesis .

At 1% level of significance there was not sufficient evident to reject the claim.